The Manchester United pair Paul Pogba and Romelu Lukaku during the match against Manchester City. Accusations of underperforming in big games can hardly be levelled at Pogba now.
Photograph: Simon Stacpoole/Offside/Getty Images

It was a shot heard around the world. First Cristiano Ronaldo leapt, twisted and arched his back, as if performing the Fosbury flop. Then came the crack of boot on ball, lace on leather, delirium and endless dissection.

But while Ronaldo’s stunning bicycle kick against Juventus took the breath away, watching him deliver in the Champions League – and again in the Madrid derby on Sunday – came as no surprise. Nowadays he follows the line from Ecclesiastes to the letter: What has been done before will be done again.

It was also Ronaldo who came to mind during the rollicking Manchester derby on Saturday, as City were running United ragged and Paul Pogba and Romelu Lukaku were again being berated for failing to impose themselves. Because people used to say the same about Ronaldo, too: big‑game bottler; flat‑track bully; unable to dominate important games.

And while Pogba provided the perfect riposte, suddenly reverting to the omnipotent marauder of his Juve days after half-time, Lukaku remained a lumbering and largely peripheral figure in United’s comeback. He left the Etihad Stadium having failed to muster a shot on target, with the fewest touches (23) and the lowest pass completion percentage (53%) of any starter. Frankly, he was awful. Critics also noted that while Lukaku has scored 31 goals in 49 appearances for club and country this season, only one of those has come in his nine Premier League matches against the big six.

All in all, Lukaku is shaping up to be a textbook example of a flat-track bully. Except I am no longer sure such a concept exists.

We all instinctively know, of course, that scoring against better teams is harder for everyone. However, when Omar Chaudhuri, the head of football intelligence at 21st Club, analysed 15 years of Premier League scoring data, he found the differences were stark. The average forward scored 0.24 non-penalty goals per 90 minutes against sides finishing in the top six in a given season – pretty much one every four games – compared with 0.37 goals against everyone else. In other words, strikers typically score at a 35% lower rate in “big matches” – whether they are good or bad, supreme or indifferent.

Sergio Agüero is a typical case study. While the City striker averages better than a goal every two games against top-six sides excluding penalties (0.52 non‑penalty goals per 90) – better than any striker in the Premier League over the past 15 years – this is 33% lower than his rate against weaker teams (0.78 NP goals per 90).

At the moment Lukaku is a minor outlier – his scoring rate is 52% lower in big matches, worse than any other striker who has scored 80 Premier League goals since 2003. But Chaudhuri insists that United fans should not be overly concerned. His data shows there is a very strong positive correlation between goals in “big matches” and “other matches”, so it is not unreasonable to suspect that Lukaku’s cold streak will eventually correct itself.

Manchester United’s Romelu Lukaku insists he is no flat-track bully

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And Lukaku has done it in big games. During his first two full seasons in England he scored eight goals against teams that finished in the top six – and at a higher rate than in “non-big” games.

If you need further convincing that variance matters look at Ronaldo’s early record at United. During his first four years in England, he scored just seven goals in 39 big matches (ie, against a top-six Premier League team or Champions League knockout match). And while he was a winger not a centre-forward, a narrative swiftly took hold: that he underperformed in big games.

That perception has taken a long time to shake – despite winning the Champions League four times, finishing top scorer in the competition on six occasions and claiming the Ballon d’Or five times.

Yet according to Chaudhuri, while Ronaldo slightly underperformed in his early years, from 2010 to 2013 he actually scored at a higher rate in big matches (against top-four La Liga sides and Champions League knockout games). Look at the figures: nine in 11 big games in 2010‑11, 11 in 12 a year later, and 10 in nine in 2012‑13. And then, unsurprising, he reverted to less superhuman levels.

In fact, as Chaudhuri notes, labelling players based on their performances in big games makes for a great study in confirmation bias. Ronaldo has scored vital goals, so whenever he does he is labelled a “big‑game player” – ignoring the fact he has managed only one non-penalty goal in his last five against Barcelona. Lukaku is the opposite; when he does not score in a big match he is targeted – ignoring the fact he provided a goal and assist against Chelsea, or an assist against Liverpool.

Perhaps there are broader lessons for clubs, too. Managers often try to scout players based on how they play in big matches or against their own team. But this, inevitably, can lead to clubs drawing overarching conclusions.

In fact, as Chaudhuri points out, smart teams might be able to exploit this inefficiency – as players who underperform in big matches might be undervalued, because coaches think they don’t have the mentality to step up.

It is an accusation that will no longer be directed at Pogba after Saturday. As Mourinho astutely put it: “Of course, two goals in a big match, one stays in the memory of the people.”

Lukaku, meanwhile, can only hope that Mourinho alters his defensive tactics in big games – and, perhaps, for a bit of luck, too.